Free Printable Solving Trig Test Review

1.

Find the exact value of sin(2x) if sin x = 12/13 and x is in the first quadrant.

a)

120/169

b)

25/169

c)

60/169

d)

5/13

2.

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

3.

$Given\ \cos\theta=\frac{5}{13}\ and\ \frac{3\pi}{2}<\theta<2\pi\ find\ \ \cos\left(2\theta\right)$

a)

$\frac{120}{169}$

b)

$-\frac{120}{169}$

c)

$\frac{24}{26}$

d)

$\frac{10}{26}$

4.

$10\sin x\cos x=$

a)

$\sin\left(10x\right)$

b)

$\sin\left(5x\right)$

c)

$5\sin\left(2x\right)$

d)

$5\cos\left(2x\right)$

5.

Find the exact value of sin $75\degree$

a)

$\frac{\sqrt{2}+\sqrt{6}}{4}$

b)

$\frac{\sqrt{8}}{4}$

c)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

d)

$\frac{\sqrt{7}}{4}$

6.

Evaluate $\cos\ \left(90^o-x\right)$

a)

$\cos\ x$

b)

$\sin\ x$

c)

$\tan\ x$

d)

$-\cos x$

7.

$Find\ the\ exact\ value\ of\ \tan\ \frac{\pi}{12}$

Hint: $\tan\left(x+y\right)=\frac{\sin\left(x+y\right)}{\cos\left(x+y\right)}$ and $\tan\left(x-y\right)=\frac{\sin\left(x-y\right)}{\cos\left(x-y\right)}$

a)

$\frac{3-\sqrt{3}}{3+\sqrt{3}}$

b)

$\frac{1-\sqrt{3}}{1+\sqrt{3}}$

c)

$\frac{1}{\sqrt{3}}$

d)

$\frac{\sqrt{3}}{3}$

8.

Find the exact value of cos $75\degree$

a)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

b)

$\frac{\sqrt{5}+\sqrt{3}}{4}$

c)

$\frac{1}{2}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

9.

Use sum or difference angles identity to find the exact value for $\sin\ \left(-15^o\right)$

a)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

d)

$-\frac{\sqrt{3}}{2}$

10.

Use sum or difference angles identity to find the exact value for $\cos105^o$

a)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

b)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

c)

$\frac{-\sqrt{6}-\sqrt{2}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

11.

Which of the following is NOT a solution to

sin θ = √(3) / 2 ?

a)

π / 3

b)

2π / 3

c)

5π / 3

d)

7π / 3

12.

Solve sinθ = ½ on θ∈[0, 2π)

a)

θ = π / 6, 7π / 6

b)

θ = π / 6, 5π / 6

c)

θ = 5π / 6, 7π / 6

d)

θ = 7π / 6, 11π / 6

13.

Solve
cos²θ = ½
on θ∈[0, 2π)

a)

θ = π /4, 7π /4

b)

θ = π /4, 3π /4

c)

θ = 3π /4, 5π /4

d)

θ = π /4, 3π /4, 5π /4, 7π /4

14.

Solve
cosθ = - √(3)/2
on θ∈[0, 2π)

a)

θ = π /3, 2π /3

b)

θ = 2π /3, 4π /3

c)

θ = π /6, 5π /6

d)

θ = 5π /6, 7π /6

15.

a)

A

b)

B

c)

C

d)

D

16.

Solve on the interval [0,2π)

tan(x) + 1 = 2

a)

0 and π

b)

3π/4 and 7π/4

c)

π/4 and 5π/4

d)

3π/4 and 5π/4

17.

Solve on the interval [0,2π)

2 sinθ + 3 = 2

a)

π/6,2π/3

b)

7π/6

c)

7π/6, 11π/6

18.

Solve on the interval [0, 2π)

4sin²x = 3

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

19.

Solve on the interval [0, 2π)

$\frac{1}{2}\sec\left(x\right)-1=0$

a)

π/6, 5π/6

b)

π/3, 5π/3

c)

2π/3, 4π/3

d)

7π/6, 11π/6

20.

Solve on the interval [0, 2π)

2sin(x)cos(x) = √2 cos(x)

**Hint: get everything on the same side and factor**

a)

π/2, 3π/2

b)

0, π/4, 3π/4

c)

π/2, 3π/2, π/4, 3π/4

d)

No solution

21.

Solve on the interval [0, 2π)

cos²(x) + sin(x) + 1 = 0

a)

π

b)

3π/2

c)

π/6, 5π/6, 3π/2

d)

No solution

22.

Solve on the interval [0, 2π)

cos(x) + 2 = 3cos(x)

a)

0, 2π/3, 4π/3

b)

π

c)

0

d)

No solution

23.

Which of these is equivalent to

2cos²(x) − 3cos(x) = 0 ?

a)

-cos²x = 0

b)

cosx(2cosx + 3) = 0

c)

cosx(2cosx − 3) = 0

d)

cos x = ⅔

24.

Which is a correct way to solve the equation

cos(x)[2cos(x) − 3] = 0?

a)

divide cos x from both sides

b)

set each factor equal to 0 and solve

c)

distribute cosx into the parentheses

d)

guess and hope for the best

25.

To solve this equation, cos²(x) + sin(x) = 1, replace cos²(x) with

a)

1/(sec²x)

b)

sin²x − 1

c)

1 − sin²x

d)

1 + tan²x

26.

Factor 0 = sin²(x) − sin(x)

a)

0 = sinx(sinx)

b)

0 = sinx(1 − sinx)

c)

0 = cosx(sinx − 1)

d)

0 = sinx(sinx − 1)

27.

True or False?

csc²(x) = 2 is equivalent to sin²(x) = ½

a)

True

b)

False

28.

Factor: sec²(x) − sec(x) − 2

a)

(sec x)(secx − 2)

b)

(secx − 2)(secx − 1)

c)

(secx − 2)(secx + 1)

d)

(secx + 2)(secx − 1)

29.

Solve for x

don't forget $\cot\left(x\right)=\frac{\cos\left(x\right)}{\sin\left(x\right)}$

a)

π

b)

π/3

c)

π/2

d)

-π

30.

a)

A

b)

B

c)

C

d)

D

31.

Solve: $2\sqrt{3}\sec\theta\ +\ 4\ =\ 0$
State all solutions in the interval [0, 2π)

a)

π /3, 2π/3

b)

2π /3, 4π/3

c)

π /6, 5π/6

d)

5π /6, 7π/6

32.

Solve equation for $0\le\theta<2\pi$ .
$2=-4-3\csc\theta$

a)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6}$

b)

$\theta=\frac{\pi}{3}$

c)

$\theta=\frac{7\pi}{6},\frac{11\pi}{6}$

d)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6},\frac{11\pi}{6}$

33.

Solve equation for $0\le\theta<2\pi$ .
$-1-2\sec^2\theta=-3\sec^2\theta$

a)

$\theta=0,\pi,\frac{4\pi}{3}$

b)

$\theta=0$

c)

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=0,\pi$

34.

Solve equation for $0\le\theta<2\pi$ .
$3\tan^2\theta\ -1\ =\ 0$

a)

$\theta=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$

c)

$\theta=\frac{\pi}{6},\frac{7\pi}{6}$

d)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

35.

$Solve\ \ 2\sin^2x\ +\ \sin x\ -\ 1\ =\ 0\ \ for\ 0\ \le\ x\ <\ 2\pi$

a)

$\frac{\pi}{6},\ \frac{\pi}{2},\ \frac{5\pi}{6}$

b)

$\frac{\pi}{2},\ \frac{7\pi}{6},\ \frac{11\pi}{6}$

c)

$\frac{\pi}{6},\ \frac{5\pi}{6},\ \frac{3\pi}{2}$

d)

$\frac{7\pi}{6},\ \frac{3\pi}{2},\ \frac{11\pi}{6}$

36.

$Solve\ \ \cos x\ \tan x\ +\ \cos x\ =\ 0\ \ for\ 0\ \le\ x\ <\ 2\pi$

a)

$\frac{\pi}{4},\ \frac{\pi}{2},\ \frac{5\pi}{4},\ \frac{3\pi}{2}$

b)

$0,\ \frac{3\pi}{4},\ \pi,\ \frac{7\pi}{4}$

c)

$\frac{\pi}{2},\ \frac{3\pi}{4},\ \frac{3\pi}{2},\ \frac{7\pi}{4}$

d)

$0,\ \frac{\pi}{4},\ \pi,\ \frac{5\pi}{4}$

37.

Solve the equation. Restrict your answer to [0,2π).

$-2\sqrt{2}=4\sin3\theta$

a)

$\left\{\frac{\pi}{24},\frac{13\pi}{24},\frac{7\pi}{12},\frac{25\pi}{24},\frac{29\pi}{24},\frac{5\pi}{4},\frac{7\pi}{4}\right\}$

b)

$\left\{\frac{7\pi}{12},\frac{25\pi}{24},\frac{13\pi}{12},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$

c)

$\left\{\frac{25\pi}{24},\frac{41\pi}{24},\frac{7\pi}{4}\right\}$

d)

$\left\{\frac{5\pi}{12},\frac{7\pi}{12},\frac{13\pi}{12},\frac{5\pi}{4},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$

38.

State the solutions in the interval $\left[0,\ 2\pi\right)$
$3\tan3x\ -\ \sqrt{3}\ =\ 0$

a)

$\frac{\pi}{18},\ \frac{7\pi}{18},\ \frac{13\pi}{18},\ \frac{19\pi}{18},\ \frac{25\pi}{18},\ \frac{31\pi}{18}$

b)

$\frac{\pi}{18},\ \frac{13\pi}{18},\ \frac{25\pi}{18}$

c)

$\frac{7\pi}{18},\ \frac{19\pi}{18},\ \frac{31\pi}{18}$

d)

$\frac{\pi}{9},\ \frac{4\pi}{9},\ \frac{7\pi}{9},\ \frac{10\pi}{9},\ \frac{13\pi}{9},\ \frac{16\pi}{9}$

39.

Solve the equation over the interval $\left[0,2\pi\right)$ . Choose all correct answers!

$\cos\left(2x\right)=-\frac{1}{2}$

a)

$\frac{\pi}{3}\ and\ \frac{5\pi}{3}$

b)

$\frac{2\pi}{3}\ and\ \frac{4\pi}{3}$

c)

$\frac{\pi}{6}\ and\ \frac{11\pi}{6}$

d)

$\frac{5\pi}{6}\ and\ \frac{7\pi}{6}$

e)

$\frac{3\pi}{4}\ and\ \frac{5\pi}{4}$

40.

Simplify the trig expression.

a)

tan²x

b)

-tan²x

c)

cot²x

d)

cos²x*sin²x

41.

Simplify the trig expression.

a)

sinx

b)

cosx

c)

cotx

d)

tanx

42.

Simplify the trig expression.

a)

secx

b)

cotx

c)

sec²x

d)

tan²x

43.

Simplify

a)

secθ

b)

cos²θ

c)

sin²θ

d)

sin²θ/cos²θ

Solving Trig Test Review

Total questions: 43

Worksheet time: 2hrs 58mins

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